#### Topics from this paper

#### 41 Citations

The Axiom of Infinity and transformations j: V -> V

- Mathematics, Computer Science
- Bull. Symb. Log.
- 2010

A new approach for addressing the problem of establishing an axiomatic foundation for large cardinals is suggested, using Lawvere's transformation, rather than ω, as a starting point for a reasonably natural sequence of strengthenings and refinements, leading to a proposed strong Axiom of Infinity. Expand

Large Cardinals and Determinacy

- 2011

The developments of set theory in 1960’s led to an era of independence in which many of the central questions were shown to be unresolvable on the basis of the standard system of mathematics, ZFC.… Expand

Executing Gödel’s programme in set theory

- Mathematics
- 2017

The study of set theory (a mathematical theory of infinite collections) has garnered
a great deal of philosophical interest since its development. There are several reasons
for this, not least… Expand

The Role of Axioms in Mathematics

- Mathematics
- 2008

To answer the question of whether mathematics needs new axioms, it seems necessary to say what role axioms actually play in mathematics. A first guess is that they are inherently obvious statements… Expand

On the Hierarchy of Natural Theories

- Mathematics
- 2021

It is a well-known empirical phenomenon that natural axiomatic theories are pre-well-ordered by consistency strength. Without a precise mathematical definition of “natural,” it is unclear how to… Expand

REMARKS ON THE GÖDELIAN ANTI-MECHANIST ARGUMENTS

There is no question that Gödel’s two incompleteness theorems (Gödel, 1931)1 are deep and important mathematical results which have significant philosophical implications (e.g., Raatikainen, 2005).… Expand

Gödel's program for new axioms: why, where, how and what?

- Mathematics
- 1996

Summary. From 1931 until late in his life (at least 1970) Godel called for the pursuit of new axioms for mathematics to settle both undecided number-theoretical propositions (of the form obtained in… Expand

Fragmentation at the Foundation

- Chemistry
- 2018

The standard axiomatization of set theory known as ZFC provides maybe the most widely accepted foundation for mathematics. But there are natural mathematical statements, such as Cantor’s continuum… Expand

V = L and Intuitive Plausibility in set Theory. A Case Study

- Computer Science, Mathematics
- The Bulletin of Symbolic Logic
- 2011

A view of intuitiveness in set theory that assumes it to hinge basically on mathematical success is formulated, and accounts of set theoretic axioms and theorems formulated in non-strictly mathematical terms are presented. Expand

A Formal Apology for Metaphysics

- 2019

There is an oldmeta-philosophical worry: very roughly, metaphysical theories have no observational consequences and so the study of metaphysics has no value. The worry has been around in some form… Expand

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Publisher Summary This chapter presents axiom of determinateness and discusses certain infinite games with perfect information. It is a mathematically interesting problem to decide which games are… Expand

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1 In his [1965] and elsewhere (for example, his [1972]), Nelson Goodman proposed some troubling examples which raise fundamental questions about our inductive practices. Let us define the predicate… Expand

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Mathematical axioms have traditionally been thought of as obvious or self-evident truths, but current set theoretic work in the search for new axioms belies this conception. This raises… Expand

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The description for this book, Contributions to the Theory of Games (AM-40), Volume IV, will be forthcoming.

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